ABSTRACT
PEI-KEE LIN Department of Mathematics, University of Memphis, Memphis TN 38152
Let £ be a Kothe-Bochner function space over [0, 1] or N . Recall a Banach space E is said to be a -complete if every order bounded sequence in E has a least upper bound. E is said to be order continuous (cr -order continuous) if for any downward directed set (sequence) [ha}a£a in E with a«€aha = 0, lim<*_»A \\ha \\ = 0. A Banach lattice E is said to be KB-space if each bounded monotone sequence in the unit ball of E is convergent. It is known that
(1) Every Kothe funcion space is o -complete. (2) Any or -complete Banach lattice E which is not order continuous contains a copy
of too • Hence if E is a Kothe function space which is not order continuous, then it contains a copy of i <*> [13, Proposition l.a.7].
